Transient Analysis of Electrical Circuits using Block Backward Differentiation Formula

Transient is the time-varying currents and voltages resulting from the sudden change in supply current or voltage. This phenomenon usually occurs due to any switching, interrupting, short-circuiting as well as any rapid changes in the structure of an electrical circuit. To avoid any damage in certain components resulting from the transient, it is important to analyze the change of voltage or current across the circuit elements. This paper studies the transient analysis of a second order RLC circuit that consists of resistors (R) and two energy storage elements, which are inductor (L) and capacitor (C). Such circuit is normally represented in the form of second order ordinary differential equations (ODEs) and such problems are not easily solved analytically. Therefore, a numerical method, namely block backward differentiation formula (BBDF) is applied for solving the ODEs by taking into consideration the damping factor and change in charge with respect to time. This method has the advantage that in each application, the solution is computed at two points simultaneously, which can give faster solutions to the problem. Numerical experiments are carried out to evaluate the capability of the proposed method. It is shown that the numerical solutions approximate the analytical solutions. The performance of the BBDF is compared with the Euler's method, Heun's method and Runge-Kutta method in terms of accuracy. Results obtained show that the proposed method is reliable for transient analysis of electrical circuit due to its comparable degree of accuracy.